Get out a cast iron skillet that's large enough for the tenderloin. If your tenderloin is really large, it might need to go into the oven to finish cooking. Make sure it’s an oven-safe pan. If the tenderloin is extra large, finish cooking in a preheated 375°F (190 °C) oven until it reaches 120-130 °F (49-54 °C).
Heat the pan over high heat until piping hot.
Add the oil, swirl it around, and when it starts to shimmer, add the meat to the pan.
Sear the tenderloin over medium-high or high. All stoves are different - if you’re on high and it’s burning, turn it to medium-high. Once there's a crust, usually after about 2-3 minutes, flip and continue searing the other sides of the meat. If you try to turn it and the meat isn’t easily coming off of the pan, that means it’s not ready.
It should only be cooked to 120-130 °F (49-54 °C) and will rise to about 130-135 °F (54-57 °C) as it rests out of the pan. It's very important not to overcook it as it'll turn tough.
Remove the pan from the oven and remove the meat to a plate. Let the meat rest for about 5-15 minutes or until it reaches 130-135 °F (54-57 °C).
Meanwhile, put the pan (with the pan drippings) back on the stove at medium-low heat and add all the herb butter ingredients. Use a wooden spatula to deglaze the pan (scrape up the flavorful bits stuck to the bottom of the pan). Cook until the garlic is soft, about 1-3 minutes.
Cut into 1 to 1.5” medallions and pour the sauce over the meat.
Cool leftovers, place in an airtight container, and refrigerate for up to 3-4 days.